Binary linear programming formulations for a multiple bin size dual bin packing problem for wood reuse optimization

We consider the two-stage two-dimensional multiple bin size dual bin packing problem applied to wood reuse. Unsplittable wooden slats are assembled into strips of minimum length to build as many wooden panels of different dimensions as possible. The dual bin packing problem is also known in the literature as the bin covering problem. Moreover, we study a one-dimensional simplification of the problem where the wooden slats can be split into two strips, which is a variable-sized bin covering problem. This article proposes a binary linear formulation for both problems. These formulations are tested on realistic field data. Computational experiments are performed to assess the impact of the cuts proposed and to compare the two formulations with respect to the proportion of wood reused, the running times, and the gaps of the solution after one hour. The results are then discussed in terms of the panel types produced and the impact of demand constraints.